Science, Models, And Squeaking Lead

At the dawn of the 14th century the Franciscan alchemist Paul of Taranto crouched over the strange lump of metal he'd created. He gaped, in awe of what he had done. It should have been impossible. The scholars told him he was a fool to even try, yet he'd done it. It wasn't gold that he'd created. He was still far from achieving that goal, but he'd made an important step. According to the book he would later publish under the title Summa perfectionis magisterii, Paul—writing under a deliberately confusing pseudonym—had just transmuted Lead into Tin!¹

For those of us in the 21st century, it's second nature to dismiss this sort of claim as obviously ridiculous. There is no known, chemical way to do what Paul intends. But that begs a very obvious question: what had he done? If we take the man at his word, he certainly seems to have done something to his bar of lead, but what? And why did he believe his experiment had succeeded?

These questions will lead us down a very fascinating path, and one that reveals the striking truth about our knowledge of the natural world.

Theory & Practice

We take so much for granted these days about the knowledge of the natural world. We consider obvious and teach to children what took generations of the brightest minds to figure out, and it can be very easy to forget that.

Today we break apart systems to understand them; this is Reductionism. And we use material analysis to understand and manipulate the properties of physical objects: that is we melt, dissolve, chemically alter, and then recombine materials in order to create what we want. But in order to do all that—and better to make predictions about what exactly our methods will accomplish in doing so—we must accept the following assumption: that an object is nothing more than a physical assortment of indivisible components.² This assumption may seem obvious to most people today, but it wasn't always that way! Indeed most serious philosophers in the past considered the idea ludicrous.³

I won't go into the history of Classical & Medieval Matter Theory, but suffice it to say that before a pre-modern version of what we today would call Atomic Theory would emerge, the dominant view of "What is Stuff?" was far more qualitative than quantitative. For the programmers out there, think of their Matter Theory as a sort of Duck Typing.⁴

If it walks like a duck and it quacks like a duck, then it's a duck.

Matter was it's qualities. Gold is yellow, ductile, resists being tarnished. Lead tarnishes easily, it's heavy. Tin is silvery and when you bend it, it squeaks. Therefore the process of turning one metal into another is a matter of giving it the desired qualities!

Photos: mine

As at every point in history, there were differing view points about what exactly matter is made of and scholarly opinions differed greatly. However, one theory—preferred by alchemists like our old friend Paul—held that the four prime elements were bound together into a duopoly of two higher-level substances to make the metals. What were those substances? Why sulfur and mercury!

Yup, literal sulfur (or brimstone) and mercury (or quicksilver).

Now before we make fun of Paul too much (or rather Geber as he called himself in his writing), let's try to understand why he thought sulfur and mercury were the foundational elements underpinning all metals. Under this theory, the difference between say lead and gold was simply in the relative proportions of these primary ingredients!

Paul, like so many alchemists, was seemingly quite the avid experimentalist, and so based his theories on what he could determine by the fire. Among many other experiments, he noticed the sulfurous smell given off by impure metals during refining and assumed that such a smell was due to a volatile sulfur within the metal itself. Additionally, according to Dr. William Newman:

The fact that calcined [i.e. burned] metals often appear in the form of yellow, red, or white powder (what we coul call oxides) suggests to Geber that they also contain...sulfur that remains after the volatile sulfur has been forced out by calcination.
- Atoms & Alchemy by William R. Newman, p. 33

As for the mercury, that brings us back to our earlier tale. Again Newman writes:

Geber proves [his] point by washing lead with quicksilver and then melting it. whereupon the lead gains the creak that the tin had lost—as he puts it, the lead is converted to tin.
- Atoms & Alchemy by William R. Newman, p. 33

According to his theory this worked because tin had more intrinsic mercury than lead. Therefore, to transform it, one simply needed to add mercury into the lead. Sure enough, once lead is washed in this way, it squeaks when it bends. Paul had successfully imparted the quality of squeakability into his lead, thereby transforming it (albeit partly) into tin.

It might sound silly, but consider this: here was a person who formed a hypothesis about the cause of a natural phenomenon, then tested it. It worked, so he built on it. That sounds a lot like science, doesn't it?

What Even is Science?

At it's core, modern science is two things: a process of inquiry and a collection of knowledge. Together those two form a model of the natural world that we use to make predictions and offer explanations into the workings of nature. Science does not, and cannot, tell us how nature actually works under the hood, instead it gives us the tools to develop and test our models.

This point is worth belaboring, because for me, it took a long time to really click.

I studied aerospace engineering, which is basically Newton's mechanics, material design, and a lot of stuff about how fluids flow (air is a fluid, you see). When you study physics in this way, it can be tempting to believe you've learned something about nature, but what you've learned is how to model nature. There are always error terms sticking out, gaps in the theory, losses you approximate (spherical, frictionless cows for example). The math isn't nature, it's an approximation. Crucially, it's an approximation that seems to work, or at least it does within your measure of tolerance.

It's hard to remember that we don't really know how nature works. We know how to approximate it. But that fact becomes easier to understand when you approach the study of nature, not from our current perspective, but from the outside.

What's so fascinating to me about the example of poor old Geber/Jabir/Paul above is that his theories about matter were utterly wrong, and yet they did offer testable predictions that were sometimes correct! Like many scientists before and since, Paul may have very well chalked up his experimental failures to defects in apparatus, hidden variables like mineral origins, or even the incompleteness of his own theories, but nevertheless he worked with and improved his theories so to arrive at testable methods and predictions, and he wasn't the only one!

It fascinates me so much because I find myself wondering: what do we believe about nature that future generations will look back on with the same bemusement that we feel about Paul of Taranto or any other proto-scientist who's theories fell short? What about nature will become so obvious that it's taught to ten-year-olds in four centuries, but that now our brightest cannot see?